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1. A list of all members of the population from which we can choose a sample is called a frame, and the potential sample members are called sampling units
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
2. A probability sample is a sample in which the sampling units are chosen from the population by means of a random mechanism such as a random number table.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
3. We can measure the accuracy of judgmental samples by applying some simple rules of probability. This way, judgmental samples are not likely to contain our built-in biases.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
4. Simple random samples are samples in which every possible sample of size n from the population has the
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same probability of being chosen.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
5. A simple random sample is one where each member of the population has a known chance (this may differ from one member to another) or probability of being chosen.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
6. In systematic sampling, one of the first k members is selected randomly, and then every kth member after this one is selected. The value k is called the sampling interval and equals the ratio N / n, where N is the population size and n is the desired sample size.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
7. In stratified sampling, the population is divided into relatively homogeneous subsets called strata, and then random samples are taken from each stratum.
a. True
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b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
8. In stratified sampling with proportional sample sizes, the proportion of each stratum selected differs from stratum to stratum.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
9. In cluster sampling, the population is divided into subsets called clusters (such as cities or city blocks), and then a random sample of the clusters is selected. Once the clusters are selected, we typically acquire information from all of the members in each selected cluster.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
10. The primary advantage of cluster sampling is sampling convenience (and possibly less cost). The downside, however, is that the inferences drawn from a cluster sample can be less accurate, for a given sample size, than for other sampling plans.
a. True
b. False
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ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
11. The finite population correction factor is a correction for the standard error when the sample size is fairly large relative to the population size.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
12. Simple random sampling can result in under-representation or over-representation of certain segments of the population. This is one of several reasons that simple random samples are almost never used in real applications.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
13. Stratified samples are typically not used in real applications because they provide less accurate estimates of population parameters for a given sampling cost.
a. True
b. False
ANSWER: False
POINTS: 1
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DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
14. Cluster sampling is often less convenient and more costly than other random sampling methods.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
15. One obvious advantage of stratified sampling is that we obtain separate estimates within each stratum –which we would not obtain if we took a simple random sample from the entire population. A more important advantage is that we can increase the accuracy of the resulting population estimates by using appropriately defined strata.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
16. Systematic sampling is generally similar to simple random sampling in its statistical properties.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
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TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
17. The standard error of sample mean is large when the observations in the population are spread out (large ), but that the standard error can be reduced by taking a smaller sample.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
18. When we sample less than 5% of the population, the finite population correction factor; fpc = , is used to modify the formula for the standard error of the sample mean.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
19. A point estimate is a single numeric value, a “best guess” of a population parameter, calculated from the sample data.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
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DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
20. The difference between the point estimate and the true value of the population parameter being estimated is called the estimation error
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
21. A confidence interval is an interval calculated from the population data, where we strongly believe the true value of the population parameter lies.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
22. The sampling distribution of any point estimate (such as the sample mean or proportion) is the distribution of the point estimates we would obtain from all possible samples of a given size drawn from the population.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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23. An unbiased estimate is a point estimate such that the mean of its sampling distribution is equal to the true value of the population parameter being estimated.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
24. The standard error of an estimate is the standard deviation of the sampling distribution of the estimate. It measures how much estimates from different samples vary.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
25. The standard error of the estimate measures how much estimates vary from sample to sample.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
26. It is customary to approximate the standard error of the sample mean by substituting the sample standard deviation s for in the formula: SE( ) = .
a. True
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b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
27. An estimator is said to be biased if the mean of its sampling distribution is not equal to the value of the population parameter being estimated.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
28. Estimation is the process of inferring the value of an unknown population parameter using data from a random sample drawn from the population.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
29. The central limit theorem (CLT) states that the sampling distribution of the mean is approximately normal, no matter what the distribution of the population, as long as the sample size is large enough.
a. True
b. False
ANSWER: True
POINTS: 1
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DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
30. When the sample size is greater than 5% of the population, the formula for the standard error of the mean should be modified with a finite population correction.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
31. A sample of size 20 is selected at random from a population of size N If the finite population correction factor is 0.9418, then N must be 169.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
32. The sampling distribution of the mean will have the same mean as the original population from which the samples were drawn.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
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TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
33. The sampling distribution of the mean will have the same standard deviation as the original population from which the samples were drawn.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
34. Nontruthful responses is an example of a nonsampling error.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
35. Voluntary response bias occurs when the responses to questions do not reflect what the investigator had in mind.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
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DATE MODIFIED: 3/29/2019 2:11 PM
36. If the sample size is greater than 30, the Central Limit Theorem (CLT) will always guarantee that the sampling distribution of the sample mean is approximately normal.
a. True
b. False
ANSWER: False
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
37. The central limit theorem (CLT) says that as long as the sample size is reasonably large, there is about a 95% chance that the magnitude of the sampling error for the mean will be no more than two standard errors.
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
38. The size of a sample can be selected by first determining the desired standard error and then using the formula to calculate n
a. True
b. False
ANSWER: True
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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39. A sample in which the sampling units are chosen from the population by means of a random mechanism is a sample.
a. probability
b. judgmental
c. convenience
d. voluntary response
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
40. A judgmental sample is a sample in which the
a. sampling units are chosen using a random number table.
b. quality of sampling units judged before they are added to the sample.
c. sampling units are chosen according to the sampler’s judgment.
d. sampling units condemn the sampling method used.
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
41. Potential sample members, called sampling units, may be
a. people.
b. companies.
c. households.
d. all of these choices.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
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OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
42. In sampling, a population is
a. the set of all humans.
b. the set of all members about which a study intends to make inferences.
c. the set of all members from whom data was collected.
d. a random group of individuals, households, cities, or countries.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
43. A list of all members of the population is called a
a. sampling unit.
b. probability sample.
c. frame.
d. relevant population
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-2 Sampling Terminology
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
44. A sample chosen in such a way that every possible subset of same size has an equal chance of being selected is called a _____sample.
a. cluster
b. systematic random
c. simple random
d. stratified random
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
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HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
45. The sampling method in which a population is divided into blocks and then selected by choosing a random mechanism is called a sampling.
a. systematic random
b. simple random
c. stratified
d. cluster
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
46. Which of the following is not a consideration when determining appropriate sample size?
a. the cost of sampling
b. the timely collection of the data
c. interviewer fatigue
d. the likelihood of nonsampling error
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
47. Identifiable subpopulations within a population are called
a. clusters.
b. samples.
c. blocks.
d. strata.
ANSWER: d
POINTS: 1
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DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
48. The defining property of a simple random sample is that
a. every possible sample of a particular size has the same chance of being chosen.
b. it is the easiest method to access samples that are chosen.
c. it requires the fewest samples necessary for statistical significance.
d. every kth subject is chosen as a sample.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
49. Selecting a random sample from each identifiable subgroup within a population is called sampling.
a. simple random
b. systematic
c. stratified
d. cluster
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
50. Which of the following are reasons for why simple random sampling is used infrequently in real applications?
a. Samples can be spread over a large geographic region.
b. Simple random sampling requires that all sampling units be identified prior to sampling.
c. Simple random sampling can result in underrepresentation or overrepresentation of certain segments of the population.
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d. All of these choices are valid reasons.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
51. Which statement is true of proportional sample sizes?
a. The proportion of a stratum in the sample is independent of the proportion of that stratum in the population.
b. The proportion of a stratum in the sample is the same as the proportion of that stratum in the population.
c. The proportion of a stratum in the sample is greater than the proportion of that stratum in the population.
d. The proportion of a stratum in the sample is less than the proportion of that stratum in the population.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
52. The probability of being chosen in a simple random sample of size n from a population of size N is
a. 1/N.
b. N – 1/n.
c. N/n.
d. n/N.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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53. The key to using stratified sampling is
a. identifying the strata.
b. selecting the appropriate strata.
c. defining the strata.
d. randomizing the strata.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
54. If systematic sampling is chosen as the sampling technique, it is probably because
a. systematic sampling has better statistical properties than simple random sampling.
b. systematic sampling is more convenient.
c. systematic sampling always results in more representative sampling than simple random sampling.
d. systematic sampling gives every possible sample of the same size from the population an equal chance of being selected.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
55. Which of the following statements correctly describe estimation?
a. It is the process of inferring the values of known population parameters from those of unknown sample statistics.
b. It is the process of inferring the values of unknown sample statistics from those of known population parameters.
c. It is the process of inferring the values of known sample statistics from those of unknown population parameters.
d. It is the process of inferring the values of unknown population parameters from those of known sample statistics.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
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TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
56. A sampling error is the result of
a. measurement error.
b. nonresponse bias.
c. nontruthful responses.
d. "unlucky" sampling.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
57. The standard deviation of is usually called the
a. standard error of the mean.
b. standard error of the sample.
c. standard error of the population.
d. randomized standard error.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
58. When a portion of the sample does not respond to the survey, has occurred.
a. a measurement error
b. nonresponse bias
c. a sampling error
d. systematic failure
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
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HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
59. The accuracy of the point estimate is measured by its
a. standard deviation.
b. standard error.
c. sampling error.
d. nonsampling error.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
60. The sampling mean is the estimate for the population mean .
a. random
b. point
c. simple
d. interval
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
61. Non-truthful response is a particular problem when
a. sensitive questions are asked.
b. surveys are anonymous.
c. interviewers are not trained.
d. the sample is from an unusual population.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
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QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
62. Measurement error occurs when
a. a portion of the sample does not respond to the survey.
b. the sample responses are not clear.
c. the responses to question do not reflect what the investigator had in mind.
d. the investigator does not correctly tally all responses.
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
63. The two basic sources for error when using random sampling are error.
a. sampling and selection
b. identification and selection
c. sampling and nonsampling
d. bias and randomness
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
64. Sampling error is evident when
a. a question is poorly worded and results in bias.
b. the sample is too small.
c. the sample is not random.
d. the sample mean differs from the population mean.
ANSWER: d
POINTS: 1
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DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
65. The opportunity for sampling error is decreased by
a. larger sample sizes.
b. smaller sample sizes.
c. affluent samples.
d. interviewer selected samples.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
66. The theorem that states that the sampling distribution of the sample mean is approximately normal when the sample size n is reasonably large is known as the theorem.
a. central limit
b. central tendency
c. simple random sample
d. point estimate
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
67. There is an approximately _____% chance that any particular will be within two standard deviations of the population mean ( ).
a. 90
b. 95
c. 99
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d. 99.7
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
68. Which of the following statements are correct?
a. A point estimate is an estimate of the range of a population parameter.
b. A point estimate is a single value estimate of the value of a population parameter.
c. A point estimate is an unbiased estimator if its standard deviation is the same as the actual value of the population standard deviation.
d. All of these choices are correct.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
69. An unbiased estimator is a sample statistic
a. used to approximate a population parameter.
b. which has an expected value equal to the value of the population parameter.
c. whose value is usually less than the population parameter.
d. that arises from samples that are of size 30 or fewer.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
70. Which of the following statements is correct?
a. A confidence interval describes a range of values that is likely not to include the actual population
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b. A confidence interval is an estimate of the range for a sample statistic.
c. A confidence interval is an estimate of the range of possible values for a population parameter.
d. A confidence interval describes a range of values that will always include the actual population parameter.
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
71. The approximate standard error of the sample mean is calculated as
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
72. The approximate 95% confidence interval for a population mean is a.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
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OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
73. The finite population correction factor, , should generally be used when
a. N is any finite size.
b. n is less than 5% of the population size N.
c. n is greater than 5% of the population size N.
d. n is any finite size.
ANSWER: c
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
74. The central limit theorem (CLT) is generally valid for
a. n > 5.
b. n > 10.
c. n > 30.
d. any size n.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
75. The averaging effect means that as you average more and more observations from a given distribution, the variance of the average
a. increases.
b. decreases.
c. is unaffected.
d. could either increase, decrease, or stay the same.
ANSWER: b
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Remember
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QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
76. The mean of the sampling distribution of always equals:
a. the population mean
b. / n.
c. the population standard deviation
d. / n.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
77. The opportunity for nonsampling error is larger when the
a. sample size is large.
b. sample size is small.
c. population size is small.
d. population size is large.
ANSWER: a
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISCB: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
78. The central limit theorem (CLT) is considered to be an important result in statistics because
a. the CLT allows us to assume that the population distribution is approximately normal, provided n is reasonably large.
b. the CLT allows us to estimate the population mean without knowing the exact form of the population distribution, provided n is reasonably large.
c. the CLT allows us to construct confidence intervals for the population mean without knowing the exact form of the population distribution, provided n is reasonably large.
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d. of all of these choices.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Understand
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
79. Consider the frame of 50 full-time employees of Computer Technologies, Inc (CTI). CTI’s human resources manager has collected annual salary figures for all employees and she has calculated a mean of $52,723, a median of $48,082 and a standard deviation of $24,167. A simple random sample of 10 employees is presented below (salary is in $1,000’s). Compute the mean, median, and standard deviation for the sample and compare these statistics with the measures for the entire company.
Population parameters: mean = $52,723, median = $48,082, standard deviation = $24,167
The sample mean and median are nearly the same as the corresponding population mean and median, but the sample standard deviation is much smaller than the population standard deviation.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
80. A sales manager for a company that makes commercial ovens for restaurants is interested in estimating the average number of restaurants in all metropolitan areas across the entire country. He does not have access to the data for each metropolitan location, so he had decided to select a sample that will be representative of all such areas, and will use a sample size of 30. Do you believe that simple random sampling is the best approach to obtaining a representative subset of the metropolitan areas in the given frame? Explain. If not, recommend how the sales manager might proceed to select a better sample of size 30 from this data?
ANSWER: Using a simple random sample may not be the best approach. If you are trying to determine the number of restaurants in metropolitan areas, it seems as though this would be somewhat dependent on the size (population) of the metropolitan areas
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under investigation. It may be better to stratify the samples. You could divide the metropolitan areas into several strata based on their population and then sample within each stratum. This may be more representative of the metropolitan areas across the country.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
The manager of a small computer company has collected current annual salaries and number of years of postsecondary education for 52 full-time employees. The data are shown below:
Current annual salaries:
Number of years of post-secondary education:
81. (A) Compute the mean, median, and standard deviation of the annual salaries for the 52 employees in the given frame.
(B) Use Excel® to choose a systematic sample of size 13 from the frame of annual salaries.
(C) Compute the mean, median, and standard deviation of the annual salaries for the 13 employees included in your systematic sample in (B)
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(D) Compare your statistics in (C) with your computed descriptive measures for the frame in (A). Is your systematic sample representative of the frame with respect to the annual salary variable?
(E) Assume that we wish to stratify these employees by the number of years of post-secondary education, select such a stratified sample of size 15 with approximately proportional sample sizes.
(F) Compute the mean, median, and standard deviation of the annual salaries for the 15 employees included in your stratified sample in (E).
(G) Compare these statistics in (F) with your computed descriptive measures for the frame obtained in (A). Is your stratified sample representative of the frame with respect to the annual salary variable?
ANSWER:
(A) The mean, median, and standard deviation of the given frame were computed using StatTools as shown below:
(B) In order to generate a systematic sample, we must first divide the frame size by the desired sample size to find the relevant intervals from which we will sample. The sampling interval in this case is 4, meaning that every 4th salary will be included in the sample. Next, we randomly choose a number between 1 and 4. Suppose that this number happens to be 1. This will be our starting point in the first block of 4 salaries To identify every 4th salary thereafter, we first developed an index column to assign an index value to each salary. We then used the MOD function in Excel® to label every 4th salary with a "1" in column C. Lastly, we used an IF statement to identify every value that has a "1" assigned to it. We have now generated a systematic sample of size 13. The sample consists of the following values shown below (read across rows):
(D) After generating the summary measures for both the frame and the sample, we can conclude that the sample does not represent the frame well. The mean, median, and standard deviation of the frame are all much smaller than the mean, median, and standard deviation of the sample.
(E) This portion of the solution involves several steps. First, we noted the total sample size needed. Second, we developed the strata we will use to separate the given frame: in this case we placed every two years in a new stratum as shown below. Next, we generated a column labeled "Category", to place a number between 1 and 5 next to the salary that corresponds with the stratum of that
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number. For example, if the annual salary was of a person who only had 2 years of education beyond secondary education, then a number 2 for Stratum 2 was placed next to the salary. The "Category" column was generated using an IF statement. We then unstacked the categories in order to count the number of salaries in each stratum. This was done by using StatTools's Data Utilities/Unstack function. Once this was completed, we used the COUNT function in Excel® to count the number of values in each stratum and then generated proportional numbers for each stratum with respect to the size of the given population. Once the proportions are generated, we used the random number function in Excel® to assign a random number to each salary. Then, by using Excel® to sort the salaries in each stratum by their random number (in this case by ascending number) we selected the salaries in each stratum that will be included in the sample. These salaries are shown below.
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(G) When looking at the mean, median, and standard deviation of both the sample and population, we can conclude that the stratified sample represents the population fairly well, although the summary measures are all slightly lower than those of the population.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_96_102
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
Suppose that you are an entrepreneur interested in establishing a new Internet-based auction service. Furthermore, suppose that you have gathered basic demographic information on a large number of Internet users. You currently have information on 1000 individuals related to their gender, age, education, marital status, annual household income, and number of people in household. Assume that these individuals were carefully selected through stratified sampling.
82. (A) To assess potential interest in your proposed enterprise, you would like to conduct telephone interviews with a representative subset of the 1000 Internet users. How would you proceed to stratify the given frame of 1000 individuals to choose 50 for telephone interviews? Explain your approach.
(B) Explain how you could apply cluster sampling to obtain a sample size of 50 from this frame. What are the advantages and disadvantages of employing cluster sampling in this case?
ANSWER:
(A) Which of these factors will have an impact on the use of the auction service? You may want to use gender, age, and annual household income. You should attempt to gather data on individuals that represent the different gender, age, and annual income groups that represent your customers. You may find that you have different responses between these groups.
(B) You may decide that you want to sample 50 people in your immediate area. You can use your local phone directory and call customers in your area. This type of sampling is convenient and is less costly. The drawback is that the inference drawn from this type of sample may not be representative of the entire population. Cluster sampling is most effective when the clusters are small scale replicas of the population as a whole.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_94_95
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TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
A statistics professor has just given the final examination in his introductory statistics course. In particular, he is interested in learning how his class of 50 students performed on this exam. The data are shown below.
83. (A) Using these 50 students as the frame, use Excel® to generate a simple random sample of size 10 from this frame.
(B) Compute the mean scores in the frame and the simple random sample you generated in (A).
(C) Compare the mean scores you computed in (B). Is your simple random sample a good representative of the frame? Why or why not?
(D) Using these 50 students as the frame, use Excel® to generate a systematic sample of size 10 from this frame.
(E) Compare the mean scores in the frame with that in the systematic sample in (D). What do you conclude?
ANSWER:
In order to solve this problem, we first generated an index value for each score in the given frame. Then we used StatTool’s Random Sample tool in the Data Utilities section to generate a simple random sample of scores from the population. Lastly, we used VLOOKUP function to find the corresponding score for each index value. This process resulted in the following sample:
(B) Population mean score = 78.92, Sample mean score = 79.90 in the above case.
(C) The mean of the sample generated from the given frame of scores is clearly very close to the mean of the population. Therefore we may conclude that the simple random sample is fairly representative of the population of introductory statistics final exam scores.
(D) In order to generate a systematic sample, we must first divide the frame size (50) by the desired sample size (10) to find the relevant intervals from which we will sample. The sampling interval in this case is 5, meaning that every 5th score will be included in the sample. Next, we randomly choose a number between 1 and 5. Suppose that this number happens to be 1. This will be our starting point in the first block of 5 scores. To identify every 5th score thereafter, we first developed an index column to assign an index value to each score. We then used the MOD
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function in Excel® to label every 5th score with a “1” assigned to it. We have now generated a systematic sample of size 10. The sample consists of the following values: 78, 72, 83, 79, 75, 90, 88, 84, 74, and 84.
(E) The means of the frame and of the sample were found to be 78.92 and 80.7, respectively. We see that these means are very close. From this analysis, we can conclude that the systematic sample is fairly representative of the frame or population.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_86_90
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
A university bookstore manager is mildly concerned about the number of textbooks that were under-ordered and thus unavailable two days after the beginning of classes. The manager instructs an employee to pick a random number, go to the place where that number book is shelved, examine the next 50 titles, and record how many titles are unavailable.
84. (A) Technically, this process does not yield a random sample of the books in the store. Why not?
(B) How could a truly random sample be obtained?
ANSWER:
(A) For true random sampling, all possible combinations of 50 books must have equal probability of being sampled. In this process, books that are shelved far from each other could not be in the same sample. Thus not all combinations would have equal probability; some combinations would have probability 0.
(B) Obtain an inventory list of all book titles and number the books. Use a table of random numbers (or computer generated random numbers) to select 50 books to be examined.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_110_111
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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Sally Bird of Big Rapids Realty has received data on 60 houses that were recently sold in Mecosta County in Michigan. The data are recorded in the table shown below. Included in this data set are observations for each of the following variables:
The appraised value of each house (in thousands of dollars)
The selling price of each house (in thousands of dollars)
The size of each house (in hundreds of square feet)
The number of bedrooms in each house
85. (A) Suppose that Sally wishes to examine a representative subset of these 60 houses that has been stratified by the number of bedrooms. Use Excel® to assist her by finding such a stratified sample of size 10 with proportional sample sizes.
(B) Explain how Sally could apply cluster sampling in selecting a sample of size 15 from this frame.
(C) What are the advantages and disadvantages of employing cluster sampling in this case?
ANSWER:
(A) In this problem, the stratified sample was found by using strata that were based on the number of bedrooms in the house. Once we established how to stratify the frame, we unstacked the prices according to the strata (in this case, the number of bedrooms). This was done by using StatPro’s Data Utilities/Unstack variables. Once this was completed, we counted the number of houses in each stratum and then assigned a proportional size to each stratum relative to the size of the frame (in this case, size of the frame is 60). After the proportions were generated, we used Excel to generate a random number for each price in each stratum. Next, we used the sort function in Excel® to place the prices in order of ascending random numbers. We then chose the prices to be included in the stratified sample. These results are shown below. Note that the stratified sample size is 11 (not 10) due to rounding.
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(B) In this situation, Sally could have selected a few neighborhoods within Mecosta County, Michigan, and obtained all the sample information from the selected neighborhoods.
(C) By using cluster sampling, Sally would be able to generate her sample more quickly and conveniently. The disadvantage of cluster sampling in this case is that Sally would have to make sure she selected neighborhoods that fairly represented the variety of households in the county. Cluster samples are the most effective when the clusters are small scale replicas of the population. For example, if the county had a large variety of homes with only 2 bedrooms, but the sample neighborhoods selected mostly contained homes with 4 bedrooms, the sample information would not fairly represent the entire frame. If this were the case, cluster sampling would not be a good way to select a sample.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_103_105
TOPICS: A-Head: 7-3 Methods for Selecting Random Samples
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
Suppose that the average weekly earnings for employees in general automotive repair shops is $450, and that the standard deviation for the weekly earnings for such employees is $50. A sample of 100 such employees is selected at random.
86. (A) Find the mean and standard deviation of the sampling distribution of the average weekly earnings in the sample.
(B) Find probability that the mean of the sample is less than $445.
(C) Find the probability that the mean of the sample is between $445 and $455.
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(D) Find the probability that the mean of the sample is greater than $460.
(E) Explain why the assumption of normality about the distribution of the average weekly earnings for employees was not involved in the answers to (A) through (D).
ANSWER:
(A) E( ) = = 450, and SE( ) = = 5
(B) P( < 445) = P(Z < -1) = 0.5000 – 0.3413 = 0.1587
(C)
(D) P( > 460) = P(Z > 2.0) = 0.5000 – 0.4772 = 0.0228
(E) The sample size is large; n = 100 is greater than 30, so the distribution of the average weekly earnings for employees is at least approximately normal.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_112_116
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
An editor of a local newspaper is concerned with the number of errors that are found in the daily paper. In order to understand the extent of this problem, the editor would like to estimate the average number of errors in the daily paper. The frame in this case is the number of errors found in the daily paper for the past six months (180 issues).
87. (A) What sample size would be required for the production personnel to be approximately 95% sure that their estimate of the average number of errors per issue is within 4 errors of the true mean? Assume that the editor’s best estimate of the population standard deviation ( ) is 10 errors per issue.
(B) How does your answer to (A) change if the editor wants the estimate to be within 3 errors of the actual population mean? Explain the difference in your answers to (A) and (B).
ANSWER: (A)
(B) In this case, This shows that we need almost twice as many observations to decrease the absolute error from 4 to 3.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_92_93
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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A columnist for the LA Times is working to meet a deadline on a story about commuting in Los Angeles. She wants to include information about the current price of gasoline in the Los Angeles metro area, but her source person for this type of information has already gone home for the day. So, she decides to take her own sample as she drives home, writing down the prices she observes as she makes her way from downtown to her neighborhood in the suburbs. Below is the data sample she obtains (units are $/gallon).
88. (A) Do you think she has obtained a true random sample?
(B) What average price could she report, based on the above sample?
(C) What is the 95% confidence interval for the average price range, based on the above sample?
(D) Do you see any issues with the 95% confidence interval calculated in part (C)?
ANSWER:
(A) For a true random sample, all possible gas stations in the LA metro area must have an equal chance of being sampled. In this case, only the stations on her route home were sampled, although they do at least represent a variety of settings (different parts of town). Given her time constraints, this sample may suffice, though.
(B) The sample mean is $3.23.
(C) Using the sample mean and sample standard deviation (0.185), the 95% confidence interval for the true mean price is approximately $3.15/gallon to $3.30/gallon.
(D) The sample, in addition to perhaps not being truly random, may also be too small to justify using the assumptions used calculating the range in (C). Typically we want n>30 unless the population data is approximately normal as well.
POINTS: 1
DIFFICULTY: Easy | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_117_120
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
Auditors of Old Kent Bank are interested in comparing the reported value of customer savings account balances with their own findings regarding the actual value of such assets. Rather than reviewing the records of each savings account at the bank, the auditors decide to examine a representative sample of savings
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account balances. The frame from which they will sample is shown below.
89. (A) What sample size would be required for the auditors to be approximately 95% sure that their estimate of the average savings account balance at this bank is within $150 of the true mean? Assume that their best estimate of the population standard deviation is $300.
(B) Choose a simple random sample of the size found in (A).
(C) Compute the observed sampling error based on the sample you have drawn from the population. How does the actual sampling error compare to the maximum possible probable absolute error established in (A)? Explain ANSWER:
(A)
(B) The simple random sample of size 16 was generated using StatTool’s Random Sample tool in the Data Utilities section. Next, the VLOOKUP function was used to place the appropriate balances next to the customers that were selected to be included in the sample. The following sample was obtained.
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11 85.92
68 87.08
(C)
Based on the above sample (results will differ):
The sample mean = $593.39
The frame mean = $537.31
The sampling error is the difference between the sample mean and the frame mean. In this case, the sampling error is $56.08, which is much less than the maximum probable absolute error of $150. This is the case because the maximum probable absolute error is, by definition, the largest possible amount that will still give 95% certainty. As illustrated here, the observed sampling error is smaller than the largest possible error.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_83_85
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
90. A cannery claims that its sardine cans have a net weight of 8 oz., with a standard deviation of 0.1 oz. You take a simple random sample of 30 cans and encounter a sample mean of 7.85 oz. Does this provide convincing evidence to reject the claimed weight of 8 oz?
ANSWER: The sampling distribution of is normal (since n30) with mean and standard deviation given by E() = = 8, and SE() = = 0.0183, respectively. Therefore, P( < 7.8) = P(Z < -8.2) = 0. If the claim were true, such a sample would not be encountered. We have convincing evidence to reject the cannery’s claim.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
The manager of a local fast-food restaurant is interested in improving service provided to customers who use the restaurant’s drive-up window. As a first step in the process, the manager asks his assistant to record the time (in minutes) it takes to serve a large number of customers at the final window in the facility’s drive-up system. The given frame in this case is 200 customer service times observed during the busiest hour of the day for this fast-food restaurant. The frame of 200 service times yielded a mean of 0.881. A simple random sample of 10 from this frame is presented below.
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91. (A) Compute the point estimate of the population mean from the sample above. What is the sampling error in this case? Assume that the population consists of the given 200 customer service times.
(B) Compute the point estimate of the population standard deviation from the sample above.
(C) Should you use the finite population correction (fpc) factor to estimate the standard error of ? Explain. If your answer is yes, what is the value of the fpc?
(D) Determine a good approximation to the standard error of the mean in this case.
ANSWER:
(A) Sample mean = 0.96. Then, sampling error = 0.96 – 0.881 = 0.079
(B) s = 0.1963
(C) Yes, we should use the finite population correction factor in this case, since a sample size of 10 is 5% of population size of 200. Here fpc = = 0.9771.
POINTS: 1
DIFFICULTY: Moderate | Bloom’s: Apply
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_106_109
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
A manager at a battery manufacturing company wants to estimate the average number of defective (or dead) batteries contained in a box shipped by the company. Production personnel at this company have recorded the number of defective batteries found in each of the 2000 boxes shipped in the past week.
92. (A) What sample size would be required for the production personnel to be approximately 95% confident that their estimate of the average number of defective batteries per box is within 0.3 unit of the true mean? Assume that the best estimate of the population standard deviation ( ) is 0.9 defective batteries per box.
(B) How does your answer to (A) change if the production personnel want their estimate to be within 0.5 unit of the actual population mean? Evaluate the tradeoff between required accuracy and sample size requirement for this case and the case in (A).
ANSWER: (A)
(B) In this case, This shows that we need almost 3 times as many observations to reduce the absolute error from 0.5 to 0.3 units. However, 36 is still a relatively small sample, and may be with it to keep the absolute error within 0.3 units.
POINTS: 1
DIFFICULTY: Challenging | Bloom’s: Analyze
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
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STUDENT ENTRY MODE: Basic
PREFACE NAME: SA_81_82
TOPICS: A-Head: 7-4 Introduction to Estimation
OTHER: BUSPROG: Analytic | DISC: Statistical Inference
DATE CREATED: 1/14/2019 12:09 PM
DATE MODIFIED: 3/29/2019 2:11 PM
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